The Role of Interest Rates and Productivity Shocks in

Emerging Market Fluctuations

∗

Mark Aguiar

University of Rochester

Gita Gopinath

Harvard University and NBER

April 6, 2007

Abstract

In this paper we use a quantitative model to explore the potential frictions that

distinguish emerging market business cycles from developed small open economies. Fol-

lowing Aguiar and Gopinath (2007) we allow total factor productivity (TFP) to have a

stationary and an integrated component. We also allow for shocks to the consumption

and investment Euler Equations that operate through the interest rate. These “wedges”

represent changes in the intertemporal marginal rate of transformation, which may be

due to changes in observed interest rates, unobserved borrowing constraints, or other

financial frictions. We estimate the model using data from Mexico and Canada. We

show that interest rate shocks orthogonal to domestic TFP fail to explain the behav-

ior of emerging markets. We then allow for interest rates to respond to/co-vary with

productivity shocks. We find that emerging market business cycles appear to be driven

by large shocks to trend income combined with relatively small transitory shocks that

co-vary with the interest rate.∗mark.aguiar@rochester.edu, gopinath@harvard.edu. Prepared for the Tenth Annual Conference of the

Central Bank of Chile, “Current Account and External Financing,” to be held in Santiago, Chile, November

9 and 10, 2006. We thank Claudio Radatzz, Manuel Marfan and Kevin Cowan for very useful comments.

We also thank Deepa Dhume for excellent research assistance.

1

1 Introduction

Business cycles in Emerging Markets are characterized by high levels of volatility in income,

investment and net exports. Consumption is more volatile than income and net exports are

highly counter-cyclical. These facts are summarized in Aguiar and Gopinath (2007, hence-

forth AG (2007)). Further, the interest rates faced by these economies are highly volatile

and negatively correlated with income. These features of the interest rate process are sum-

marized in Neumeyer and Perri (2005). In this paper we adopt a standard stochastic small

open economy business cycle model and allow the economy to be driven by productivity

shocks that have permanent and transitory components as well as by shocks to the interest

rate process. We then estimate the role of the different processes in explaining the business

cycle behavior of emerging markets.

In AG (2007), we examined an economy driven exclusively by shocks to productivity.

Productivity shocks in this context may be viewed as manifestations of deeper frictions in

the economy such as changes in monetary, fiscal and trade policies. For instance, Restuccia

and Schmitz (2004) provide evidence of a 50% drop in productivity within five years in the

petroleum industry in Venezuela following its nationalization in 1975. Similarly, Schmitz

and Teixeira (2004) document almost a doubling of productivity in the Brazilian Iron-Ore

Industry following its privatization in 1991. It is such dramatic changes in productivity

following reforms and undoing of reforms that we view as characterizing emerging markets.

In addition, several emerging markets experience terms of trade shocks that display a high

degree of persistence. In this set-up we provided a methodology for identifying the role of

transitory versus trend shocks in explaining business cycles. The procedure relied on using

the intuition behind the permanent income hypothesis.

In AG (2007), we adopted the standard small open economy assumption and modelled

the interest rate as an exogenous international risk-free rate, which we held constant. In this

environment the economy always repays its debt and there is never any default. In Aguiar

and Gopinath (2006)we allow explicitly for default in an Eaton and Gersovitz set-up. We

2

specified an endowment economy driven by trend and stationary shocks. We show that

incorporating trend shocks is important in generating empirically plausible rates of default

as well as simultaneously matching key correlations between the interest rate, output, and

the current account.

In this paper, we extend AG (2007) to allow for a stochastic interest rate process. We

will consider three specifications. The first is the case of exogenous interest rate shocks that

are independent of the productivity shocks. The second is the case where in addition to

independent shocks the interest rate responds to transitory productivity shocks. The third

case is where the interest rate also responds to trend productivity shocks. We will assume

a reduced form specification for all these processes and provide intuition for the nature of

the process.

It is important to note that we estimate the interest rate process from the Euler Equa-

tions and do not use observed interest rates. This mirrors our treatment of productivity

shocks, where we do not use the Solow residual series to directly identify the underlying

productivity process. We do this for two reasons. Firstly, the observed rates are not risk free

rates given the probability of default. The promised rate observed in the data may therefore

not be the relevant real rate governing behavior.1 Secondly, agents may be constrained in

their access to financial markets. In that case, there is an implicit Lagrange multiplier that

governs the consumption/investment decision rather than the observed market rate. Our

estimation will pick up fluctuations in this multiplier. This approach is different from the

work of Neumeyer and Perri (2005) in that NP take the observed interest rate process and

feed this into the economy. This assumes that the euler equation with repayment is always

satisfied at the observed interest rates.

We show that the model with interest rate shocks that are orthogonal to productivity

shocks does poorly in matching the features of the data for emerging market countries.

Movements in the interest rate affect consumption and investment by setting the price for1See Aguiar and Gopinath (2006), Arellano (2006), Yue (2006) for explicit models of default.

3

intertemporal substitution. An increase in the interest rate reduces consumption relative

to the future as it increases the incentive to save. It also reduces investment in physical

capital as the return from the bond is higher. Since in this exercise interest rate shocks

are orthogonal to productivity shocks, the induced correlation between consumption and

income and investment and income is low, contrary to the data. The response of output,

on impact, to a rise in the interest rate will be small as productivity has not changed and

capital takes time to adjust. Moreover, when consumption and leisure are non-separable,

labor supply rises in response to a drop in consumption which generates an increase in

output, which is counterfactual given that high interest rate periods have been associated

with large declines in output. It is clearly the case that interest rate shocks that are not

associated with movements in productivity will perform poorly in matching the facts for

emerging markets. This point is similar in spirit to the work of Neumeyer and Perri (2005)

and Chari and Kehoe (2006).

We next allow the interest rate to respond to productivity shocks—both transitory and

trend shocks. The data suggest that a high level of productivity should be associated with

a lower interest rate. A positive shock to productivity raises consumption and the increase

is amplified by the contemporaneous decline in interest rates. This increases the relative

volatility of consumption for a given income process. Also, investment increases following

the rise in productivity and decline in interest rates. This implies that net-exports decrease,

inducing a negative correlation between net exports and income. The precise moments of

the stationary distribution will depend on the persistence in the income and interest rate

process. For reasons explained below, the model performs better when the interest rate

primarily responds to the transitory income shock.

Lastly, we use GMM and data from Mexico to estimate the parameters of a model that

allows for both exogenous interest rate shocks and productivity shocks and for the interest

rate shock to respond to the transitory income shock. In the benchmark case, where the

model allows only for productivity shocks, the random walk component of the Solow residual

is estimated to be 1.02. In AG (2007) we estimate that the random walk component for

4

Canada was far lower at 0.5. When we allow for the richer specification with interest rate

shocks, we estimate the random walk component to be essentially the same at 1.01. This

supports the conclusions in AG (2007) that emerging markets are subject to more volatile

trend shocks as compared to developed markets. We also find evidence of a small negative

covariance between productivity shocks and the implied interest rate.

It is important to emphasize that the differences in the Solow residual processes be-

tween developed and emerging markets may well be a manifestation of deeper frictions in

the economy. Chari, Kehoe, and McGrattan (forthcoming), for instance, show that many

frictions, including financial frictions, can be represented in reduced form as Solow residuals.

From the perspective of private agents in our economy, these shocks appear as exogenous

shifts in productivity. Our analysis provides support for models with frictions that are re-

flected in the persistence of Solow residuals, rather than frictions that distort the response

of investment and consumption to underlying productivity. For instance, Guajardo (2007),

describes a model with financial frictions and finds that it fits the data best when there are

exogenous labor financing wedges which affect hiring decisions and are procyclical. That is,

financing working capital requirements is easier in booms as compared to recessions. These

financing wedges behave like productivity shocks. Our analysis shows that interest rate

shocks that only affect the Euler Equation add little to matching the facts in the data for

emerging markets. Clearly, one could argue that there are interest rate movements that

interact with underlying financial frictions to generate shocks that look like productivity

shocks. Our analysis is completely consistent with such a model.

We also present here evidence that Chile has features similar to other emerging markets

documented in AG (2007).2 The correlation between HP-filtered net exports as a ratio

of GDP and HP-filtered log of GDP is -0.82 for Chile. There does not exist a quarterly

series on private consumption before 1996. For the 10 years from 1996-2006 the volatility

of HP-filtered log GDP is 1.63 compared to a volatility of 1.89 for HP-filtered log of private

consumption. This is similar to other emerging markets, which on average experience2We thank David Rappoport for providing us with this data

5

consumption volatility that exceeds the volatility of income and net exports that are highly

counter-cyclical. In Section 2 we describe the stochastic growth model. In Section 3 we

describe the identification strategy and provide intuition by presenting impulse responses

to various shocks. Lastly, in Section 4 we describe the results from a GMM estimation of

the model.

2 Stochastic Growth Model

The model here is reproduced from AG (2007) and augmented to include a stochastic

interest rate process. Technology is characterized by a Cobb-Douglas production function

that uses capital, Kt, and labor, Lt, as inputs

Yt = eztK1−αt (ΓtLt)α, (1)

where α ∈ (0, 1) represents labor’s share of output. The parameters zt and Γt represent pro-

ductivity processes. The two productivity processes are characterized by different stochastic

properties. Specifically, zt follows an AR(1) process

zt = ρzzt−1 + εzt (2)

with |ρz| < 1, and εzt represents iid draws from a normal distribution with zero mean and

standard deviation σz.

The parameter Γt represents the cumulative product of “growth” shocks. In particular,

Γt = egtΓt−1 =t∏

s=0

egs

gt = (1− ρg)µg + ρggt−1 + εgt ,

where |ρg| < 1 and εgt represents iid draws from a normal distribution with zero mean and

standard deviation σg. The term µg represents productivity’s long-run mean growth rate.

We loosely refer to the realizations of g as “growth shocks” as they constitute the stochastic

6

trend of productivity. We use separate notation for shocks to the level of productivity (zt)

and the growth of productivity (gt) to simplify exposition and calibration.

Given that a realization of g permanently influences Γ, output is nonstationary with a

stochastic trend. For any variable x, we introduce a hat to denote its detrended counterpart:

xt ≡ xt

Γt−1.

Note that we normalize by trend productivity through period t − 1. This insures that if

xt is in the agent’s information set as of time t − 1, so is xt. The solution to the model is

invariant to the choice of normalization.

Period utility is Cobb-Douglas,

ut =

(Cγ

t (1− Lt)1−γ

)1−σ

1− σ(3)

where 0 < γ < 1. A well-behaved steady state of the deterministic linearized model requires

β(1 + r∗) = µ1−γ(1−σ)g .

The equilibrium is characterized by maximizing the present discounted value of utility

subject to the production function (1) and the per-period resource constraint:

Ct + Kt+1 = Yt + (1− δ)Kt − φ

2

(Kt+1

Kt− eµg

)2

Kt −Bt + qtBt+1. (4)

Capital depreciates at the rate δ and changes to the capital stock entail a quadratic adjust-

ment cost φ2

(Kt+1

Kt− eµg

)2Kt. We assume international financial transactions are restricted

to one-period, risk-free bonds. The level of debt due in period t is denoted Bt and qt is the

time t price of debt due in period t + 1.

Fluctuations in the price of debt, qt, will be our focus. We assume that the interest

rate is potentially driven by an exogenous process rt as well as the domestic TFP shocks.

Specifically, the price of debt q is given by the expression below.

7

1qt

= 1 + r∗ + e{rt+azzt+ag(gt−µg)} + ψ

[e

Bt+1Γt

−b − 1]

, (5)

where

rt = ρrrt−1 + εrt . (6)

The world interest rate is held constant at r∗. The country-specific shock to the interest rate

is given by εrt , which is orthogonal to z and g. The induced process rt has an autocorrelation

coefficient ρr and a long run mean of zero. The parameters az and ag capture the sensitivity

of the interest rate to the the transitory productivity shock and the trend productivity shock,

respectively. We should note that the correlation of the interest rate and productivity does

not imply a direction of causation between the two. See Aguiar and Gopinath (2006) for a

model in which exogenous domestic productivity shocks drive an endogenous interest rate,

while Neumeyer and Perri (2005) present a model in which exogenous (foreign) interest rate

shocks drive domestic TFP. b represents the steady-state level of debt, and ψ > 0 governs

the elasticity of the interest rate to changes in indebtedness. This sensitivity to the level

of outstanding debt, takes the form used in Schmitt-Grohe and Uribe (2003).3 In choosing

the optimal amount of debt, the representative agent does not internalize the fact that she

faces an upward-sloping supply of loans.

In normalized form, the representative agent’s problem can be stated recursively:

V (K, B, z, g, r) = max{C,L,K′,B′}

(Cγ (1− L)1−γ

)1−σ

1− σ+ βegγ(1−σ)EV (K ′, B′, z′, g′, r′)

(7)

3This adjustment is typically motivated by the need to make assets in the linearized model stationary. An

alternative is to recognize that we are linearly approximating a non-linear economy for which a stationary

distribution exists (for example, due to borrowing constraints and a world equilibrium interest that is lower

than the discount rate, as in Aiyagari 1994). Quantitatively, since the elasticity of interest rate to changes in

indebtedness is set close to 0 (0.001 to be exact), there is a negligible difference between the two approaches

in terms of the HP-filtered or first-differenced moments of the model.

8

s.t. C + egK ′ = Y + (1− δ)K − φ

2

(eg K ′

K− eµg

)2

K − B + egqB′. (8)

The evolution of the capital stock is given by,

egK ′ = (1− δ) K + X − φ

2

(K ′

Keg − eµg

)2

K. (9)

Given an initial capital stock, K0, and debt level, B0, the behavior of the economy is

characterized by the first-order conditions of the problem (7), the technology (1) and budget

(8) constraints, and the transversality conditions.

We solve the normalized model numerically by log-linearizing the first-order conditions

and resource constraints around the deterministic steady state. Given a solution to the

normalized equations, we can recover the path of the non-normalized equilibrium by mul-

tiplying through by Γt−1. We also compute the theoretical moments of the model from the

coefficients of the linearized solution.

3 Identification

The primary goal of this paper is to assess the relative importance of interest rate shocks,

transitory productivity shocks and permanent shocks to productivity in explaining the

behavior of emerging markets. In AG (2007) we described the methodology of exploiting

decisions by informed, optimizing agents to identify the underlying shock process. In this

paper, we extend that methodology to accommodate a richer process for the interest rate.

The methodology we employ selects parameters of the model to match key moments

of the data. Below, we discuss which moments are particularly useful in identifying the

parameters of interest. However, we note from the start that we do not use market interest

rates on sovereign debt. The reason is that those interest rates represent the price of a

defaultable bond. This is a different asset than that modelled above. To see this, consider

9

the Euler Equation for bonds from the above model:

β

qE

uc′

uc= 1. (10)

Note that while consumption is stochastic, the interest rate paid (conditional on information

at the time of borrowing) is deterministic. In a model with defualtable debt, the consumer

pays the interest rate conditional on no-default, and pays zero (or some fraction) if default

occurs. Therefore, the observed market interest rate cannot be used directly in a simple

Euler Equation, but must be combined with a full specification of in which states default

occurs and what payments are made conditional on default.

Our interest rate process q can be viewed as a wedge in the Euler Equations for con-

sumption and investment. Our estimation will then back out the parameters governing

the stochastic process of this wedge. In this sense, it is similar to the exercise of Chari,

Kehoe, and McGrattan (forthcoming). It also captures unobserved frictions (to a linear ap-

proximation) such as additional borrowing costs or constraints beyond the market interest

rate.

3.1 Interest Rates Shocks Orthogonal to Productivity Shocks

We begin with an exploration of uncorrelated interest rate shocks. That is, shocks to

the interest rate that are orthogonal to total factor productivity. Changes to the inter-

est rate induce changes to consumption and investment for a given path of income due to

inter-temporal substitution. This will raise the relative volatility of consumption and in-

vestment. Therefore, such shocks have the potential to explain the relatively high volatility

of consumption in emerging markets.

However, by introducing shocks that move consumption and investment independently of

income reduces the covariance of consumption and investment with income. This generates

counterfactual implications for the cyclicality of net exports.

Figure 1 plots the impulse response of consumption, investment, net exports, and income

10

to a one percent shock to εr. We set ρr = 0.9. As expected, an increase in the interest rate

leads to a drop in consumption, with an initial decline of roughly 3 percent. Investment

declines in an even more dramatic fashion. Output remains steady, declining slightly over

the path due to the lagged declines in investment. This leads to a jump in net exports.

To see how orthogonal interest rate shocks affect key moments of the simulated model,

consider a model in which we set az = ag = 0, but set σr ≡ stdev(εr) > 0. To be precise, we

consider models with various σr ranging from zero to one percent. For each environment,

we compute key moments of the simulated economy and plot them in Figure 2. We fix all

other parameters. We also set γ = 1 so that labor supply is fixed. All moments refer to HP-

filtered variables. In Panel A of Figure 2 we see how the relative variance of consumption,

investment, and net exports increases as we increase σr. This corresponds to the above

intuition. In Panel B, we see that net exports become more pro-cyclical as we increase σr.

This takes us further from the data. Correspondingly, consumption, investment become less

correlated with income. This is because a positive interest rate shock lowers consumption

and investment. As TFP has not changed, this reduces the correlation with income. In fact,

when consumption and leisure are nonseparable, the decreased consumption is associated

with higher labor and therefore higher income, inducing a negative correlation between

consumption and income. In this set-up, a crisis which is associated with a large increase

in interest rates, will reduce consumption but raise output, which is completely counter-

factual.

It is clearly the case that exogenous interest rate shocks will do poorly in explaining

the behave of emerging markets. It will be hard to generate the large counter-cyclicality in

the current accounts and the much larger responsiveness of consumption relative to income.

This argument is in line with the results in Neumeyer and Perri (2005) and Chari and Kehoe

(2006). A model where the interest rate process does not show up as affecting productivity

will have little hope of matching moments of the business cycle.

11

3.2 Interest Rate that Co-vary with Productivity Shocks

From the previous section it is clear that we need to interact the interest rate shock with

the productivity shock. As we have two productivity processes, there are two dimensions

along which we can link the interest rate and productivity. We begin by setting ag = 0 and

considering the link between transitory productivity shocks and the interest rate. We then

set az equal to 0 and assume the interest rate responds only to the permanent shock g.

To gain some intuition, in Figure 3 we plot the impulse response of consumption and

income to a shock to εz when az = 0 and when az = −0.1. This latter case generates a fall

in the interest rate when productivity increases. This can be an implication of the Eaton

Gersovitz style models of default in which default occurs during low income realizations (see

Aguiar and Gopinath (2006) and Arellano (2004)). With persistent shocks, a high shock

today implies on average high shocks tomorrow and a correspondingly low probability of

default. This generates a negative relationship between productivity and the interest rate.

For the benchmark case of az = 0, we see the standard consumption smoothing result —

consumption increases, but income increases much more. The case of az < 0 combines the

income response with a substitution response that favors initial consumption. This generates

a larger initial jump in consumption and a subsequent declining profile of consumption.

Given the transitory nature of the shock, the net effect is that consumption tracks the

shape of the income impulse response. Not depicted is the response of investment, which

has a similar intuition as consumption.

The impulse responses indicate that allowing the interest rate and productivity to co-

move overcome some of the limitations of transitory productivity. Namely, consumption

and investment respond more to income and in a way that makes net exports negatively

associated with income. To see how this extension affects business cycle moments, we plot

the key moments as a function of az in Figure 4. As az becomes increasingly negative,

this raises the volatility of consumption relative to income. A positive productivity shock

lowers interest rates, generating an increase in consumption above and beyond the income

12

effect. Unlike the orthogonal interest rate process of Figure 2, the additional consumption

volatility increases the correlation of consumption and income. This effect is driven by the

fact that the interest rate moves one-for-one with productivity. A similar story holds for

investment. These effects make net export countercyclical, a key feature of the data for

emerging markets.

As noted above, an alternative approach is to allow the interest rate to respond to

permanent productivity shocks, i.e. ag < 0. In Figure 5 we plot the impulse response to

a shock to εg in the benchmark case and in the case when ag = −1. Given that g has a

permanent effect on income, we see that consumption responds strongly to the initial shock

in the benchmark case, exceeding the initial response of income. Allowing the interest rate

to respond as well heightens the initial response of consumption. However, subsequently,

the interest falls back quickly to its initial level as g is nearly iid. This generates a sharp

fall in consumption and then a levelling out. However, income jumps and then continues

to rise in response to a growth shock. Therefore, allowing ag < 0 lowers the correlation of

consumption with income, taking us further from the data.

This effect can be seen clearly in Figure 6. As we increase ag (in absolute value),

while the variance of consumption and investment increase, the correlations with income

at business cycle frequencies fall. This reduces the cyclicality of net exports, drawing us

further from the data.

The poor performance of the model with ag < 0 is due to the fact that growth rates have

little persistence, generating interest rates with little persistence. An alternative would be

that interest rates are a function of the level of the stochastic trend Γ. However, this would

imply a nonstationary interest rate.

13

3.3 Productivity Shocks Alone

AG (2007) considered a model in which ag = az = 0. We briefly summarize the intuition

behind the identification of the relative variance σg/σz. In response to a transitory shock

to productivity, agents increase consumption, but by less than the increase in income since

they expect income to be lower in the future and by saving they can smooth consumption.

On the other hand, if the economy is hit by a growth shock which implies permanently

higher income and depending on the persistence of the growth shock an upward sloping

profile of income the agents will increase consumption by at least as much as the increase

in income. Therefore consumption is more volatile relative to income in the world with

permanent shocks relative to transitory shocks. This difference in the response of σc is

observed in figure 7.

Therefore, by observing the behavior of consumption we can infer the relative impor-

tance of trend versus transitory shocks. Similarly, it follows that given the response of

consumption and we should expect net exports to be far more countercyclical for the econ-

omy with trend shocks and the moment on net exports can be used to identify the underlying

productivity shock.

3.4 Identification Strategy

Given the above results, we restrict σr = ag = 0. That is, we consider a model in which

the interest rate co-varies with transitory productivity shocks and allow for both transitory

and trend shocks to productivity. The patterns depicted in figures 4 and 7 indicate how we

can identify the key parameters. Increases in the magnitude of az and σg/σz have a similar

impact on the cyclicality of the current account. However, while both raise the relative

volatility of consumption, net exports, and investment, the relationships differ. Figure 4

indicate that az has an almost linear effect on the relative variances, while figure 7 indicates

that the impact of σg/σz eventually dies out. In particular, for large enough az, the relative

14

volatility of net exports exceeds that of consumption. This reflects the differential sensitivity

of investment and consumption to interest rate shocks. Therefore, the empirical moments

of σ(c) and σ(nx) combined with the empirical covariance of net exports with output pin

down the relative magnitudes of az and σg/σz. Given the relative variance of trend and

transitory shocks, the level of income volatility then identifies the level of σz and σg.

4 Estimates

Following the above identification strategy, in this section we estimate σg, σz, and az by

matching the following (HP-filtered) moments of the data: the standard deviations of in-

come, consumption, and net exports, as well as the covariance of net exports with income.

We use data from Mexico as a representative emerging market and Canada as a repre-

sentative developed open economy. We fix other parameters at the values listed in Table

5

For each set of estimates, we report the relative importance of the random walk com-

ponent of productivity. Beveridge-Nelson (1981) showed that any I(1) series can be decom-

posed into a random walk component (denoted τ) and a stationary component. A natural

measure of the importance of the random walk component is the ratio of the variance of

the growth rate of the trend component to the growth rate of total TFP.

σ2∆τ

σ2∆TFP

=α2σ2

g

(1− ρg)2σ2∆TFP

=

α2σ2g

(1−ρg)2

[ 2σ2z

1+ρz+ α2σ2

g

1−ρ2g]

(11)

We report the estimates for σg, σz and az in Table 5. In the columns denoted “bench-

mark” we restrict az = 0. This corresponds to the benchmark model of AG (2007). The

other columns estimate az. The first two columns consider a model in which labor is sup-

plied exogenously. This corresponds to setting the Cobb-Douglas preference parameter on

consumption (γ) to one, so that leisure does not enter utility. The next two columns allow

labor supply to vary endogenously, setting γ = 0.36. The final two columns estimate the

15

model using Canadian data.

For the benchmark model using Mexican data (column 1), we see that σg is larger than

σz and that the relative contribution of the random walk component to TFP is 1.02. This is

similar to the results reported in AG (2007). In the second column of Table 2, we estimate

az along with σz and σg. We find that az < 0, although we cannot reject az = 0 at standard

significance levels. Even allowing for interest rate shocks, we estimate a relatively large σg,

with the contribution of the random walk component estimated to be 1.01.

Allowing labor supply to vary endogenously does not overturn this pattern. In both

specifications, the random walk component of productivity is estimated to be roughly 1.0.

The coefficient az is estimated to be small.

The case of Canada indicates a relatively small random walk component. In both

specifications, we estimate the relative random walk component to be 0.4. The coefficient

az is also estimated to be small and not significantly different from zero.

In Table 5 we report the implied business cycle moments from the estimated models

along with the corresponding empirical moments from Mexico and Canada. The implied

moments for Mexico correspond to the first two columns of Table 5. In respect to Mexico,

we see that both models perform well in matching key features of the data. The empirical

relative volatility of consumption is 1.3, while the models with and without interest rate

shocks both generate relative variances of 1.1. The cyclicality of net exports is -0.8 in the

data and is -0.7 and -0.6 in the models without and with interest rate shocks, respectively.

In general, allowing for interest rate shocks does not markedly improve the fit of the model.

A similar story holds for Canada, as seen in the final columns of Table 5.

In the specification with interest rate shocks, we see that interest rates are countercyclical

in Mexico and procyclical in Canada. However, the variance of the implied interest rates

is negligible. This reflects that while consumption is volatile in emerging markets, it is not

driven by inter-temporal substitution, but rather by income shocks.

16

5 Discussion and Conclusion

Emerging Markets are characterized by large volatility in their income and consumption

and large countercyclicality in net exports as compared to developed small open economies.

They also face a volatile interest rate process that is negatively correlated with the level of

GDP in these economies. There is a large amount of literature that attempts to explain

these features of the data and infer the importance of productivity and interest rate shocks

in explaining the patterns observed in the data. In this paper we perform a similar exercise

by extending the framework in AG(2007) which allowed only for productivity shocks to one

that allows for a richer specification of interest rate shocks and for the interaction between

productivity and interest rate shocks.

One finding, which supports other evidence in the literature, is that interest rate shocks

that do not effect productivity cannot be the main explanation for the business cycles

of emerging markets. These markets are characterized by large movements in output at

business cycle frequencies that are associated with large movements in the Solow resid-

ual. Accordingly, interest rate shocks alone will do little to explain these large movements

in output. It is important to uncover channels through which interest rate shocks affect

productivity.

If the interest rate is negatively correlated with the productivity shock, then interest

rates can indeed play an important role. It can explain, at least qualitatively, a consump-

tion process that is more volatile than income and counter-cyclical net exports. When we

estimate the model to allow for the interaction between interest rates and productivity we

find a small negative correlation between productivity and interest rates. We also find that,

even in this framework, we obtain a large role for trend shocks which supports the main

result in AG (2007), namely, that an important characteristic of emerging markets is that

shocks to trend productivity play a predominant role in explaining movements at business

cycle frequencies, unlike developed markets.

17

In this paper we have taken a reduced form approach to modelling both the interest

rate process and productivity shocks. Future work should examine the structural features of

emerging markets that give rise to the particular form of these processes. In AG (2006) we

explore a model with Eaton-Gersovitz style endogenous default. While this approach does

generate default in equilibrium and can generate a countercyclical interest rate process, it

fails to generate sufficient volatility in the market interest rate process. Further research is

required to understand the source of the volatility in the interest rate process.

18

References

[1] Aguiar, Mark and Gita Gopinath (2006). “Defaultable Debt, Interest Rates and the

Current Account.” Journal of International Economics, 69(1): 64-83.

[2] Aguiar, Mark and Gita Gopinath (2007). “Emerging Market Business Cycles: The

Cycle is the Trend,” Journal of Political Economy, Vol 115,1, 69–102.

[3] Aiyagari, S. Rao (1994), “Uninsured Idiosyncratic Risk and Aggregate Saving,” The

Quarterly Journal of Economics, Vol 109, 3, 659-684.

[4] Arellano, Cristina and Enrique Mendoza (2002). “Credit Frictions and ‘Sudden Stops’

in Small Open Economies: An Equilibrium Business Cycle Framework for Emerging

Market Crises.” NBER Working Paper No. w8880.

[5] Backus, David, Patrick J. Kehoe and Finn. E. Kydland (1995). “International Business

Cycles: Theory and Evidence.” Frontiers of Business Cycle Research. ed. Thomas F.

Cooley. Princeton University Press. Princeton, New Jersey.

[6] Bergoeing, Raphael, Timothy Kehoe, Patrick Kehoe and Raimundo Soto (2002). “A

Decade Lost and Found: Mexico and Chile in the 1980s.” Review of Economic Dynam-

ics, 5 , 166-205.

[7] Bernanke, Ben and Refet Gurkaynak (2002). “Is Growth Exogenous? Taking Mankiw,

Romer and Weil Seriously.” NBER Macroeconomics Annual 16:11-57.

[8] Beveridge, Stephen, and Charles R. Nelson (1981). “A New Approach to Decomposition

of Economic Time Series into Permanent and Transitory components with Particular

attention to the Measurement of the Business Cycle.” Journal of Monetary Economics

7(2):151-74.

[9] Blundell, Richard and Ian Preston (1998), “Consumption Inequality and Income Un-

certainty,” Quarterly Journal of Economics, 113(2): 603-640.

19

[10] Calvo, Guillermo A. (1986), “Temporary Stabilization: Predetermined Exchange

Rates,” Journal of Political Economy, 94(6): 1319-1329.

[11] Calvo, Guillermo A. and Carmen Reinhart (2000). “When Capital Inflows come to

a Sudden Stop: Consequences and Policy Options.” in Peter Kenen and Alexandre

Swoboda. “Key Issues in Reform of the International Monetary and Financial System.”

Washington DC: International Monetary Fund: 175-201.

[12] Campbell, John and Angus Deaton (1989). “Why is Consumption so Smooth?” Review

of Economic Studies. 56(3) July:357-373.

[13] Chari, V.V., Patrick Kehoe and Ellen McGrattan (forthcoming), “Business Cycle Ac-

counting, ” Econometrica.

[14] Cochrane, John (1988). “How Big is the Random Walk in GNP?” Journal of Political

Economy 96(5) October:893-920.

[15] Cochrane, John (1994). “Permanent and Transitory Components of GNP and Stock

Prices.” Quarterly Journal of Economics 109(1) February:241-265.

[16] Correia, Isabel, Joao C. Neves, Sergio Rebelo (1995). “Business Cycles in Small Open

Economies.” European Economic Review 39(6) June:1089-1113.

[17] Dornbusch, Rudiger and Sebastian Edwards (1992). “Macroeconomics of Populism in

Latin America.” NBER Conference Volume.

[18] Greenwood, Jeremy, Zvi Hercowitz and Gregory W. Hoffman (1988). “Investment,

Capacity Utilization, and Real Business Cycle.” American Economic Review 78(3)

June:402-17.

[19] Hamilton, James (1994), Time Series Analysis, Princeton University Press, Princeton,

NJ.

[20] Hansen, Lars (1982). “Large Sample Properties of Generalized Method of Moments

Estimators.” Econometrica 50(4):1029-1054.

20

[21] Mendoza, Enrique (1991). Real Business Cycles in a Small Open Economy. American

Economic Review 81(4) September:797-818.

[22] Neumeyer, Pablo A. and Fabrizio Perri (2005). “Business Cycles in Emerging Markets:

The Role of Interest Rates.” Journal of Monetary Economics 52(2): 345-380.

[23] Restuccia, Diego and Schmitz, James (2004) ”Nationalization’s Impact on Output and

Productivity: The case of Venezuelan Minerals”, working paper.

[24] Schmitt-Grohe, Stephanie and Martin Uribe (2003). “Closing Small Open Economy

Models.” Journal of International Economics 61(1) October:163-185.

[25] Schmitz, James and Teixeira, Arilton (2004), “Privatization’s Impact on Private Pro-

ductivity: The case of Brazilian Iron Ore”, working paper.

[26] Standard and Poor’s, (2000). Emerging Stock Markets Factbook 2000 McGraw Hill

Company. New York, NY.

[27] Stock, James H. and Mark W. Watson (2003). “ Understanding Changes in Interna-

tional Business Cycle Dynamics.” NBER Working Paper no. w9859.

21

Table 1: Benchmark Parameter Values

Time Preference Rate β 0.98

Coefficient of Relative Risk Aversion σ 2

Cobb-Douglas Utility Parameter γ 1, 0.36

Steady State Debt to GDP b 10%

Coeff. on Interest Rate Premium Ψ 0.001

Labor Exponent (Production) α 0.68

Depreciation Rate δ 0.05

Capital Adjustment Cost φ 1.5

Persistence in z process ρz 0.95

Persistence in g process ρg 0.01

22

Table 2: Estimates

Mexico Canada

Exogenous Labor Endogenous Labor Endogenous Labor

Benchmark With az Benchmark With az Benchmark With az

σz 0.13 0.16 0.13 0.24 0.72 0.69

(2.42) (0.79) (0.66) (1.06) (0.09) (0.16)

σg 2.78 2.70 2.69 2.68 0.84 0.89

(0.44) (0.33) (0.00) (0.31) (0.15) (0.09)

az -0.40 -0.01 0.01

(1.85) (0.55) (0.02)

Random Walk 1.02 1.01 1.01 1.00 0.39 0.44

Component (0.18) (0.08) (0.05) (0.15) (0.07) (0.13)Notes: Estimates obtained from matching empirical moments of Mexico and Canada for respective columns. Moments

used were standard deviation of HP-filtered log income, log consumption, and net exports/GDP as well as the

covariance of HP-filtered net exports/GDP and log income. Exogenous Labor model sets γ = 1. Endogenous Labor

model sets γ = 0.36.

23

Table 3: Implied Moments

Mexico Canada

Data Model I Model II Data Model I Model II

σ(y) 2.40 2.69 2.63 1.55 1.56 1.55

σ(c)/σ(y) 1.26 1.09 1.10 0.74 0.71 0.72

σ(nx)/σ(y) 0.90 0.74 0.84 0.57 0.59 0.60

σ(i)/σ(y) 4.15 3.52 3.81 2.67 3.23 3.13

σ(r) NA 0.08 NA 0.01

ρ(yt, yt−1) 0.82 0.78 0.78 0.90 0.79 0.79

ρ(c, y) 0.92 0.98 0.98 0.87 0.87 0.85

ρ(nx, y) -0.75 -0.68 -0.61 -0.12 -0.17 -0.13

ρ(i, y) 0.91 0.86 0.82 0.74 0.85 0.84

ρ(r, y) NA -0.01 NA 0.90Notes: Empirical moments and implied moments from alternative models. Model I and Model II

for Mexico correspond respectively to the first two columns of estimates (exogenous labor supply

model) of Table 2. Model I and Model II of Canada correspond to the respective columns of

estimates for Canada from Table 2.

24

Figure 1: Impulse Response to Interest Rate Shock

-20

-15

-10

-5

0

5

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

cyinx

Note: Impulse response to a 1 percent shock to εr

Figure 2: Business Cycle Moments and σr

Panel A: Standard Deviation of Investment, Consumption, and Net Exports

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

20.0

0.00% 0.10% 0.20% 0.30% 0.40% 0.50% 0.60% 0.70% 0.80% 0.90% 1.00%

stdev of log interest rate

stde

v (r

el to

inco

me) investment consumption

net exports

Note: Standard Deviation of (HP-filtered, log) consumption, investment, and net exports relative to income as a function of σr.

Panel B: Cyclicality of Investment, Consumption, and Net Exports

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-0.03 0.04 0.07 0.10 0.11 0.12 0.12 0.13 0.13 0.13 0.13

stdev of log interest rate

corr

with

inco

me

investment consumption net exports

Note: Correlation of (HP-filtered, log) consumption, investment, and net exports with income as a function of σr.

Figure 3: Impulse Response to z Shock

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

consumption_benchmarkincome_benchmarkconsumption_azincome_az

Note: Impulse response to a 1 percent shock to εz. Benchmark model sets az=0. “az” model sets az=-0.1.

Figure 4: Business Cycle Moments and az Panel A: Standard Deviation of Investment, Consumption, and Net Exports

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.00 -0.01 -0.02 -0.03 -0.04 -0.05 -0.06 -0.07 -0.08 -0.09 -0.10

a_z

stde

v (r

el to

inco

me)

investmentconsumptionnet exports

Note: Standard Deviation of (HP-filtered, log) consumption, investment, and net exports relative to income as a function of az.

Panel B: Cyclicality of Investment, Consumption, and Net Exports

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.00 -0.01 -0.02 -0.03 -0.04 -0.05 -0.06 -0.07 -0.08 -0.09 -0.10

a_z

corr

with

inco

me

investment consumption

net exports

Note: Correlation of (HP-filtered, log) consumption, investment, and net exports with income as a function of az.

Figure 5: Impulse Response to g Shock

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

consumption_benchmarkincome_benchmarkconsumption_agincome_ag

Note: Impulse response to a 1 percent shock to εg. Benchmark model sets ag=0. “ag” model sets ag=-1.

Figure 6: Business Cycle Moments and ag

Panel A: Standard Deviation of Investment, Consumption, and Net Exports

0.0

2.0

4.0

6.0

8.0

10.0

12.0

0.00 -0.10 -0.20 -0.30 -0.40 -0.50 -0.60 -0.70 -0.80 -0.90 -1.00

a_g

stde

v (r

el to

inco

me)

investment consumption

net exports

Note: Standard Deviation of (HP-filtered, log) consumption, investment, and net exports relative to income as a function of ag.

Panel B: Cyclicality of Investment, Consumption, and Net Exports

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.00 -0.10 -0.20 -0.30 -0.40 -0.50 -0.60 -0.70 -0.80 -0.90 -1.00

a_g

corr

with

inco

me

investmentconsumptionnet exports

Note: Correlation of (HP-filtered, log) consumption, investment, and net exports with income as a function of ag.

Figure 7: Business Cycle Moments and σg/σz

Panel A: Standard Deviation of Investment, Consumption, and Net Exports

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00

sigma(g)/sigma(z)

stde

v (r

el to

inco

me)

investmentconsumptionnet exports

Note: Standard Deviation of (HP-filtered, log) consumption, investment, and net exports relative to income as a function of σg/σz.

Panel B: Cyclicality of Investment, Consumption, and Net Exports

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.00 -0.10 -0.20 -0.30 -0.40 -0.50 -0.60 -0.70 -0.80 -0.90 -1.00

sigma(g)/sigma(z)

corr

with

inco

me

investmentconsumptionnet exports

Note: Correlation of (HP-filtered, log) consumption, investment, and net exports with income as a function of σg/σz.